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作者：Belloni, Alexandre; Chernozhukov, Victor
作者单位：Duke University; Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT)
摘要：We consider median regression and, more generally, a possibly infinite collection of quantile regressions in high-dimensional sparse models. In these models, the number of regressors p is very large, possibly larger than the sample size n, but only at most s regressors have a nonzero impact on each conditional quantile of the response variable, where s grows more slowly than n. Since ordinary quantile regression is not consistent in this case, we consider l(1)-penalized quantile regression (l(...
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作者：Roquain, Etienne; Villers, Fanny
作者单位：Universite Paris Cite; Sorbonne Universite
摘要：In a context of multiple hypothesis testing, we provide several new exact calculations related to the false discovery proportion (FDP) of step-up and step-down procedures. For step-up procedures, we show that the number of erroneous rejections conditionally on the rejection number is simply a binomial variable, which leads to explicit computations of the c.d.f., the sth moment and the mean of the FDP, the latter corresponding to the false discovery rate (FDR). For step-down procedures, we deri...
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作者：Koltchinskii, Vladimir
作者单位：University System of Georgia; Georgia Institute of Technology
摘要：We study a problem of estimation of a Hermitian nonnegatively definite matrix rho of unit trace (e. g., a density matrix of a quantum system) based on n i.i.d. measurements (X-1, Y-1), ... , (X-n, Y-n), where Y-j = tr(rho X-j)+ xi(j), j = 1, ... , n, {X-j} being random i.i.d. Hermitian matrices and {xi(j)} being i.i.d. random variables with E(xi(j) vertical bar X-j) = 0. The estimator (rho) over cap (epsilon) := S is an element of S-argmin [n(-1) Sigma(n)(j=1) (Y-j - tr(SXj))(2) + epsilon tr(S...
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作者：Knapik, B. T.; van der Vaart, A. W.; van Zanten, J. H.
作者单位：Vrije Universiteit Amsterdam; Eindhoven University of Technology
摘要：The posterior distribution in a nonparametric inverse problem is shown to contract to the true parameter at a rate that depends on the smoothness of the parameter, and the smoothness and scale of the prior. Correct combinations of these characteristics lead to the minimax rate. The frequentist coverage of credible sets is shown to depend on the combination of prior and true parameter, with smoother priors leading to zero coverage and rougher priors to conservative coverage. In the latter case ...
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作者：Ionides, Edward L.; Bhadra, Anindya; Atchade, Yves; King, Aaron
作者单位：University of Michigan System; University of Michigan; National Institutes of Health (NIH) - USA; NIH Fogarty International Center (FIC); University of Michigan System; University of Michigan
摘要：Inference for partially observed Markov process models has been a long-standing methodological challenge with many scientific and engineering applications. Iterated filtering algorithms maximize the likelihood function for partially observed Markov process models by solving a recursive sequence of filtering problems. We present new theoretical results pertaining to the convergence of iterated filtering algorithms implemented via sequential Monte Carlo filters. This theory complements the growi...
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作者：Seijo, Emilio; Sen, Bodhisattva
作者单位：Columbia University
摘要：In this paper we study the consistency of different bootstrap procedures for constructing confidence intervals (CIs) for the unique jump discontinuity (change-point) in an otherwise smooth regression function in a stochastic design setting. This problem exhibits nonstandard asymptotics, and we argue that the standard bootstrap procedures in regression fail to provide valid confidence intervals for the change-point. We propose a version of smoothed bootstrap, illustrate its remarkable finite sa...
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作者：Zhang, Li-Xin; Hu, Feifang; Cheung, Su Hung; Chan, Wai Sum
作者单位：Zhejiang University; Chinese University of Hong Kong; Chinese University of Hong Kong
摘要：Urn models have been widely studied and applied in both scientific and social science disciplines. In clinical studies, the adoption of urn models in treatment allocation schemes has proved to be beneficial to researchers, by providing more efficient clinical trials, and to patients, by increasing the likelihood of receiving the better treatment. In this paper, we propose a new and general class of immigrated urn (IMU) models that incorporates the immigration mechanism into the urn process. Th...
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作者：Dattner, I.; Goldenshluger, A.; Juditsky, A.
作者单位：University of Haifa; Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA)
摘要：The subject of this paper is the problem of nonparametric estimation of a continuous distribution function from observations with measurement errors. We study minimax complexity of this problem when unknown distribution has a density belonging to the Sobolev class, and the error density is ordinary smooth. We develop rate optimal estimators based on direct inversion of empirical characteristic function. We also derive minimax affine estimators of the distribution function which are given by an...
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作者：Dette, Holger; Melas, Viatcheslav B.
作者单位：Ruhr University Bochum; Saint Petersburg State University
摘要：The celebrated de la Garza phenomenon states that for a polynomial regression model of degree p - 1 any optimal design can be based on at most p design points. In a remarkable paper, Yang [Ann. Statist. 38 (2010) 2499 - 2524] showed that this phenomenon exists in many locally optimal design problems for nonlinear models. In the present note, we present a different view point on these findings using results about moment theory and Chebyshev systems. In particular, we show that this phenomenon o...
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作者：Rigollet, Philippe; Tsybakov, Alexandre
作者单位：Princeton University; Institut Polytechnique de Paris; ENSAE Paris
摘要：In high-dimensional linear regression, the goal pursued here is to estimate an unknown regression function using linear combinations of a suitable set of covariates. One of the key assumptions for the success of any statistical procedure in this setup is to assume that the linear combination is sparse in some sense, for example, that it involves only few covariates. We consider a general, nonnecessarily linear, regression with Gaussian noise and study a related question, that is, to find a lin...
